Question

SHOW WORK WILL MARK BRAINLIEST

Answer 1

Answer:

$\large\boxed{x=\dfrac{5\pi}{4}\ \vee\ x=\dfrac{7\pi}{4}}$

Step-by-step explanation:

The first step in attachment.

$\sin(x)=-\dfrac{\sqrt2}{2}\to x=-\dfrac{\pi}{4}+2k\pi\ \vee\ x=\dfrac{5\pi}{4}+2k\pi\\\\x\in[0,\ 2\pi)\\\\\text{Therefore}\\\\x=-\dfrac{\pi}{4}+2\pi=\dfrac{7\pi}{4}\ \vee\ x=\dfrac{5\pi}{4}$